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Recursive methods for estimating the radial basis function‐based state‐dependent autoregressive model
Author(s) -
Zhou Yihong,
Ding Feng,
Ji Yan,
Hayat Tasawar
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4890
Subject(s) - autoregressive model , convergence (economics) , radial basis function , nonlinear system , basis (linear algebra) , series (stratigraphy) , computer science , forgetting , function (biology) , mathematics , mathematical optimization , algorithm , estimation theory , artificial intelligence , artificial neural network , statistics , paleontology , linguistics , physics , geometry , philosophy , quantum mechanics , evolutionary biology , economics , biology , economic growth
Summary Identifying a nonlinear radial basis function‐based state‐dependent autoregressive (RBF‐AR) time series model is the basis for solving the corresponding prediction and control problems. This paper studies some recursive parameter estimation algorithms for the RBF‐AR model. Considering the difficulty of the nonlinear optimal problem arising in estimating the RBF‐AR model, an overall forgetting gradient algorithm is deduced based on the negative gradient search. A numerical method with a forgetting factor is provided to solve the problem of determining the optimal convergence factor. In order to improve the parameter estimation accuracy, the multi‐innovation identification theory is applied to develop an overall multi‐innovation forgetting gradient (O‐MIFG) algorithm. The simulation results indicate that the estimation model based on the O‐MIFG algorithm can capture the dynamics of the RBF‐AR model very well.